Theorems · Theorem · commutative algebra

LinearMap.localizedMap_surjective_iff_subsingleton_localized_coker

∀ {R : Type u_7} {M : Type u_8} {N : Type u_9} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M]
  [inst_3 : AddCommGroup N] [inst_4 : Module R N] (S : Submonoid R) (φ : M →ₗ[R] N),
  Function.Surjective ⇑((LocalizedModule.map S) φ) ↔ Subsingleton (LocalizedModule S (N ⧸ φ.range))

Defined in

Mathlib.Algebra.Module.LocalizedModule.Submodule

Cited by

1 results in Mathlib

Foundations

Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleAddCommGroupModule